Is it possible to parent bones between armatures?
There's a method of constraining that works especially well with bones, and avoids unwanted offsets caused by double transforms.

go to pose mode, select the child bone, add a "copy transform" constraint, set it to Parent armature, parent bone, local space both.
The same for the others child bones.

Consider that you can even animate the influence of the constraints.

Another way is using drivers, which are more powerful (you can program curves of influence and many others complex behaviours) but more difficult to explain in a few words; search for info about them, even in this site.